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middle diamond Rainbow sets PFA(S)[S] Closed coloring Large Cardinals Selective Ultrafilter Foundations Dushnik-Miller positive partition relation Knaster S-Space free Souslin tree Strong coloring Successor of Regular Cardinal Ostaszewski square Singular Density Almost countably chromatic OCA tensor product graph HOD Distributive tree stick Subtle tree property Subadditive Partition Relations Souslin Tree Forcing ZFC construction Amenable C-sequence polarized partition relation Almost-disjoint family Slim tree SNR Club Guessing Coherent tree square Microscopic Approach Minimal Walks Subnormal ideal Poset O-space xbox Precaliber Antichain P-Ideal Dichotomy 54G20 transformations L-space Subtle cardinal Prevalent singular cardinals Fodor-type reflection Diamond for trees Uniformly coherent Dowker space Rock n' Roll Luzin set Filter reflection PFA weak diamond Absoluteness Uniformly homogeneous unbounded function C-sequence Square-Brackets Partition Relations diamond star Almost Souslin coloring number Chang's conjecture Ulam matrix free Boolean algebra Strongly Luzin set Shelah's Strong Hypothesis projective Boolean algebra stationary reflection Chromatic number Postprocessing function Jonsson cardinal Cardinal Invariants Non-saturation indecomposable ultrafilter weak square Whitehead Problem Constructible Universe Analytic sets Hereditarily Lindelöf space Commutative cancellative semigroups super-Souslin tree AIM forcing stationary hitting very good scale Diamond-sharp Singular cardinals combinatorics specializable Souslin tree regressive Souslin tree higher Baire space Ineffable cardinal nonmeager set Mandelbrot set approachability ideal Erdos Cardinal Prikry-type forcing Hindman's Theorem Diamond Parameterized proxy principle Singular cofinality Open Access Commutative projection system Erdos-Hajnal graphs Fast club Cohen real Was Ulam right Knaster and friends Strongly compact cardinal strongly bounded groups Countryman line incompactness Rado's conjecture GMA Generalized descriptive set theory Generalized Clubs Martin's Axiom Hedetniemi's conjecture Well-behaved magma ccc Kurepa Hypothesis Intersection model Local Club Condensation. Ramsey theory over partitions Cardinal function Weakly compact cardinal Universal Sequences Sigma-Prikry Iterated forcing Nonspecial tree Vanishing levels countably metacompact Forcing Axioms Small forcing Sierpinski's onto mapping principle Ascent Path Respecting tree weak Kurepa tree Sakurai's Bell inequality sap square principles Uniformization Lipschitz reduction Aronszajn tree Reflecting stationary set Fat stationary set b-scale Successor of Singular Cardinal Greatly Mahlo club_AD reflection principles full tree Reduced Power Axiom R
Tag Archives: Singular Density
On topological spaces of singular density and minimal weight
Abstract: We introduce a weakening of the Generalized Continuum Hypothesis, which we will refer to as the Prevalent Singular cardinals Hypothesis (PSH), and show it implies that every topological space of density and weight $\aleph_{\omega_1}$ is not hereditarily Lindelöf. The assumption … Continue reading
Workshop on Set Theory and its Applications, February 2007
These are the slides of a talk given at the Workshop on Set Theory and its Applications workshop (Weizmann Institute, February 19, 2007). Talk Title: Nets of spaces having singular density Abstract: The weight of a topological space X is the … Continue reading
On the consistency strength of the Milner-Sauer conjecture
Abstract: In their paper from 1981, Milner and Sauer conjectured that for any poset $\mathbb P$, if $\text{cf}(\mathbb P)$ is a singular cardinal $\lambda$, then $\mathbb P$ must contain an antichain of size $\text{cf}(\lambda)$. The conjecture is consistent and known … Continue reading
